-LRB- CNN -RRB- -- Robin Van Persie played in a Manchester United shirt for the first time , but he could not stop his new club falling to an opening day defeat at Everton .

Marouane Fellaini powered home a near-post header in the 57th minute to ensure a 1-0 victory for the Merseyside team and an early blow for Alex Ferguson 's desire to wrestle back the English Premier League trophy from neighbors Manchester City .

And Everton 's victory was no piece of luck . It was carved out by a gritty , determined side who tried for every opportunity and won plaudits after the game for defending the lead .

Fellaini had nearly opened the scoring just seven minutes before , when he fired wide . But the second time there was no doubt and he found a gap through the defenders to get it into the center of the net .

Whilst Everton seemed to be tiring , they still held their own when Manchester United attacks came . New signing Shinji Kagawa was sending in a couple of balls for the likes of Wayne Rooney to work with , but nothing came of them .

Van Persie started the game from the substitutes ' bench , but Ferguson decided to bring on his new striker in the 68th minute as a replacement for Danny Welbeck , who was seemingly running out of ideas to break through a resolute Everton defense .

The former Arsenal player did not waste any time in trying to make a mark on his new team . Within a minute of coming on , last season 's EPL top scorer whipped in a corner kick which required an alert Everton back line to sweep clear .

But after that , Everton sat back and frustrated Manchester United 's attempts to try and get chances to the new signing . And the Goodison Park crowd were happy to see them do it .

The English Premier League was not the only league to see a shock result on Monday . In Spain , newly-promoted Deportivo La Coruna sent out a strong message on their return to La Liga by beating last season 's seventh-placed club Osasuna 2-0 .

Two loan players ensured the victory against Los Rojillos . Colombian midfielder Abel Aguilar , who normally plays for Hercules , struck in the 53rd minute of the game and the second came two minutes into time added on from Portugal striker Nelson Oliveira , who is on loan from Benfica .

Rayo Vallecano left it late before beating Granada 1-0 , with midfielder Roberto Trashorras scoring five minutes into added time .

In Germany , Bayern Munich made light work of their DFB Cup first round opponents , beating SSV Jahn Regensburg 4-0 in a Bavarian derby .

The side , who were recently promoted to the second tier of German football , managed to hold out for 32 minutes before Bayern broke the deadlock through new signing Mario Mandzukic .

Young prospect Xherdan Shaqiri replaced Franck Ribery just after halftime and scored the second a quarter of an hour after the restart .

Bayern then hit Regensburg with the final two goals 10 minutes before time when Croatia striker Mandzukic got his second and the man who replaced him , veteran Peru international Claudio Pizarro , scored number four in the 88th minute to mark the start of his second spell in Munich .

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Everton shock title hopefuls by beating Alex Ferguson 's side 1-0 in their opening game

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Robin Van Persie started on substitutes ' bench after his transfer from Arsenal

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Newly promoted Deportivo start their La Liga campaign with a shock 2-0 win over Osasuna

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Bayern Munich breeze through their first round DFB Cup tie with Jahn Regensburg